Problem: What do the following two equations represent? $4x+5y = 2$ $12x+15y = 0$
Answer: Putting the first equation in $y = mx + b$ form gives: $4x+5y = 2$ $5y = -4x+2$ $y = -\dfrac{4}{5}x + \dfrac{2}{5}$ Putting the second equation in $y = mx + b$ form gives: $12x+15y = 0$ $15y = -12x$ $y = -\dfrac{4}{5}x + 0$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.